You will find the following material useful. It contains a lab manual for the computer exercises using GAP.
1st Homework due Friday, 17th of January: Summarize what you have learnt in MATH 415A.
2nd Homework due Friday, 24th of January: Review Chapter 4 from Lay's book for MATH 215 and do problems 37 Section 23, 37 Section 26, 34, 37 Section 27 in Fraleigh's book.
3rd Homework due Friday, 31th of January: Download the computer algebra system GAP from www.gap-system.org and install it on a computer of your choice. If you need help, please talk to George Todd, the GTA for the course. Do problems 2, 10, 26 in Section 29, and 9,26,27 in Section 30 of Fraleigh's book.
4th Homework due Friday, 7th of February:8th Homework due Friday, 7th of March: Do problems 4,5,6, 11, 13 in Section 49 and problems 3,5 in Section 50 in Fraleigh's book.
9th Homework due Friday, 4th of April: Do problems 3,4,9,12,13 in Section 51 and problems 23,24,25 in Section 50 in Fraleigh's book.10th Homework due Friday, 11th of April:
Let $n \in \mathbb{N}$, $T=\{1,\dots,n\}$, and let $S_n$ be the symmetric group on $T$. Show that the set $T \times T$ is an $S_n$-set if we define $\pi * (i,j) := (\pi(i),\pi(j))$ for $\pi \in S_n$ and $i,j \in T$. Determine the $S_n$-orbits of $T \times T$.
Do problems 11,12,13,16 in Section 53, problem 20 in Section 16, and problem 6 in Section 17 in Fraleigh's book.
11th Homework due Friday, 18th of April: Do problems 17, 18(e,f,g,h), 19, 22 in Section 53 and problem 8 in Section 54.
Do the GAP exercise 33.4 and 33.5, page 96, in the GAP lab manual Also choose 5 monic rational polynomials and compute the order of their Galois groups using the GAP-function GaloisType.
12th Homework due Friday, 25th of April: Do problems 5, 12 in Section 54, problems 13,15,19,22 in Section 36, and problems 4,5 in Section 37.